Using ab-initio calculations, we study the electronic structure of gallium-doped germanium, which was found recently to be a superconductor, with a critical temperature of 0.5 Kelvins, and a particularly low density of Cooper pairs. The calculations of the electronic properties reveal that no sign of an impurity band is observed, and that the Fermi level lies in the valence band of Germanium. Moreover, the calculation of the phonon frequencies shows that a new mode associated to the Ga atom is appearing, around 175$ cm-1.
Superconductivity in group IV semiconductors is desired for hybrid devices combining both semiconducting and superconducting properties. Following boron doped diamond and Si, superconductivity has been observed in gallium doped Ge, however the obtained specimen is in polycrystalline form [Herrmannsdörfer et al., Phys. Rev. Lett. 102, 217003 (2009)]. Here, we present superconducting single-crystalline Ge hyperdoped with gallium or aluminium by ion implantation and rear-side flash lamp annealing. The maximum concentration of Al and Ga incorporated into substitutional positions in Ge is eight tim…
Ga interstitials in GaAs ($I_{Ga}$) are studied using the local-orbital {ab-initio} code SIESTA in a supercell of {216+1} atoms. Starting from eight different initial configurations, we find five metastable structures: the two tetrahedral sites in addition to the 110-split$\mathrm{_{[Ga-As]}}$, 111-split$\mathrm{_{[Ga-As]}}$, and 100-split$\mathrm{_{[Ga-Ga]}}$. Studying the competition between various configuration and charges of $I_{Ga}$, we find that predominant gallium interstitials in GaAs are charged +1, neutral or at most -1 depending on doping conditions and prefer to occupy the tetrahe…
We present a first-principles calculation of the electronic properties of crystalline silicon and gallium arsenide in a uniform electric field. Polarized Wannier-like functions which are confined in a finite region are obtained by minimizing a total-energy functional which depends explicitly on the macroscopic polarization of the solid. The polarization charge density and the electronic dielectric constant are computed via finite differences. The results coincide with those of the linear response approach in the limit of vanishing electric field and infinite localization region.
Thermodynamics and kinetics of Li, Na, and Mg storage in Ge is studied ab initio. The most stable configurations can consist of tetrahedral, substitutional, or a combination of the two types of sites. In the dilute limit, Li, Na prefer interstitial, while Mg prefers substitutional sites. At higher concentrations of Li, Na, and Mg, there is a combination of interstitial and substitutional sites. This is an important finding, as previous ab initio studies of alloying type electrode materials ignored substitutional sites. Insertion energies computed at dilute concentration (x = 1/64) show that Na…
Impurity levels and formation energies of acceptors in wurtzite GaN are predicted ab initio. Be_Ga is found to be the shallow (thermal ionization energy $\sim$ 0.06 eV); $Mg_{Ga}$ and $Zn_{Ga}$ are mid-deep acceptors (0.23 eV and 0.33 eV respectively); $Ca_{Ga}$ and $Cd_{Ga}$ are deep acceptors ($\sim$0.65 eV); $Si_N$ is a midgap trap with high formation energy; finally, contrary to recent claims, $C_N$ is a deep acceptor (0.65 eV). Interstitials and heteroantisites are energetically not competitive with substitutional incorporation.
It was previously believed that the Bloch electronic states of non-magnetic materials with inversion symmetry cannot have finite spin polarizations. However, since the seminal work by Zhang et al. [Nat. Phys. 10, 387-393 (2014)] on local spin polarizations of Bloch states in non-magnetic, centrosymmetric materials, the scope of spintronics has been significantly broadened. Here, we show, using a framework that is universally applicable independent of whether hidden spin polarizations are small (e.g., diamond, Si, Ge, and GaAs) or large (e.g., MoS2 and WSe2), that the corresponding quantity ari…
We report here a reexamination of the static properties of vacancies in GaAs by means of first-principles density-functional calculations using localized basis sets. Our calculated formation energies yields results that are in good agreement with recent experimental and {\it ab-initio} calculation and provide a complete description of the relaxation geometry and energetic for various charge state of vacancies from both sublattices. Gallium vacancies are stable in the 0, -, -2, -3 charge state, but V_Ga^-3 remains the dominant charge state for intrinsic and n-type GaAs, confirming results from …
An ab initio molecular dynamics study of femtosecond laser processing of germanium is presented in this paper. The method based on the finite temperature density functional theory is adopted to probe the structural change, thermal motion of the atoms, dynamic property of the velocity autocorrelation, and the vibrational density of states. Starting from a cubic system at room temperature (300 K) containing 64 germanium atoms with an ordered arrangement of 1.132 nm in each dimension, the femtosecond laser processing is simulated by imposing the Nose Hoover thermostat to the electronic subsystem …
We have investigated the structural sequence of the high-pressure phases of silicon and germanium. We have focussed on the cd->beta-tin->Imma->sh phase transitions. We have used the plane-wave pseudopotential approach to the density-functional theory implemented within the Vienna ab-initio simulation package (VASP). We have determined the equilibrium properties of each structure and the values of the critical parameters including a hysteresis effect at the phase transitions. The order of the phase transitions has been obtained alternatively from the pressure dependence of the enthalpy and of t…
We present an ab initio study of dopant-dopant interactions in beryllium-doped InGaAs. We consider defect formation energies of various interstitial and substitutional defects and their combinations. We find that all substitutional-substitutional interactions can be neglected. On the other hand, interactions involving an interstitial defect are significant. Specially, interstitial Be is stabilized by about 0.9/1.0 eV in the presence of one/two BeGa substitutionals. Ga interstitial is also substantially stabilized by Be interstitials. Two Be interstitials can form a metastable Be-Be-Ga complex …
We study the adsorption behavior of Ga on (0001) GaN surfaces combining experimental specular reflection high-energy electron diffraction with theoretical investigations in the framework of a kinetic model for adsorption and ab initio calculations of energy parameters. The measurement of a Ga/GaN adsorption isotherm allows the quantification of the equilibrium Ga surface coverage as a function of the impinging Ga flux. The temperature dependence is discussed within an {\em ab initio} based growth model for adsorption taking into account the nucleation of Ga clusters.
Thin-film solar cells with CuIn$_x$Ga$_{1-x}$Se$_2$ (CIGS) absorber are still far below their efficiency limit, although lab cells reach already 19.9%. One important aspect is the homogeneity of the alloy. Large-scale simulations combining Monte Carlo and density functional calculations show that two phases coexist in thermal equilibrium below room temperature. Only at higher temperatures, CIGS becomes more and more a homogeneous alloy. A larger degree of inhomogeneity for Ga-rich CIGS persists over a wide temperature range, which may contribute to the low observed efficiency of Ga-rich CIGS s…
A roadblock in utilizing InGaAs for scaled-down electronic devices is its anomalous dopant diffusion behavior; specifically, existing models are not able to explain available experimental data on beryllium diffusion consistently. In this paper, we propose a comprehensive model, taking self-interstitial migration and Be interaction with Ga and In into account. Density functional theory (DFT) calculations are first used to calculate the energy parameters and charge states of possible diffusion mechanisms. Based on the DFT results, continuum modeling and kinetic Monte Carlo simulations are then p…
We report calculated, electronic and related properties of wurtzite and zinc blende gallium nitrides (w-GaN, zb-GaN). We employed a local density approximation (LDA) potential and the linear combination of atomic orbital (LCAO) formalism. The implementation of this formalism followed the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). The calculated electronic and related properties, for both structures of GaN, are in good agreement with corresponding, experimental data, unlike results from most previous ab initio calculations utilizing a density function…
A Molecular Dynamics (MD) study of static and dynamic properties of molten and glassy germanium dioxide is presented. The interactions between the atoms are modelled by the classical pair potential proposed by Oeffner and Elliott (OE) [Oeffner R D and Elliott S R 1998, Phys. Rev. B, 58, 14791]. We compare our results to experiments and previous simulations. In addition, an ab initio method, the so-called Car-Parrinello Molecular Dynamics (CPMD), is applied to check the accuracy of the structural properties, as obtained by the classical MD simulations with the OE potential. As in a similar stud…
We have calculated (ab initio) and measured (by spin-echo techniques) the anharmonic self-energy of phonons at the X-point of the Brillouin zone for isotopically pure germanium. The real part agrees with former, less accurate, high temperature data obtained by inelastic neutron scattering on natural germanium. For the imaginary part our results provide evidence that transverse acoustic phonons at the X-point are very long lived at low temperatures, i.e. their probability of decay approaches zero, as a consequence of an unusual decay mechanism allowed by energy conservation.
We present ab initio calculations of the electronic and optical properties of hexagonal SiGe alloys in the lonsdaleite structure. Lattice constants and electronic band structures in excellent agreement with experiment are obtained using density-functional theory. Hexagonal Si has an indirect band gap, while hexagonal Ge has a pseudo-direct gap, i.e. the optical transitions at the minimum direct band gap are very weak. The pseudo-direct character of pure hexagonal Ge is efficiently lifted by alloying. Already for a small admixture of Si, symmetry reduction enhances the oscillator strength of th…
We present a self-consistent, real-space calculation of the Wannier functions of Si and GaAs within density functional theory. We minimize the total energy functional with respect to orbitals which behave as Wannier functions under crystal translations and, at the minimum, are orthogonal. The Wannier functions are used to calculate the total energy, lattice constant, bulk modulus, and the frequency of the zone-center TO phonon of the two semiconductors with the accuracy required nowadays in ab-initio calculations. Furthermore, the centers of the Wannier functions are used to compute the macros…
Polyvalent metal melts (gallium, tin, bismuth, etc.) have microscopic structural features, which are detected by neutron and X-ray diffraction and which are absent in simple liquids. Based on neutron and X-ray diffraction data and results of \textit{ab initio} molecular dynamics simulations for liquid gallium, we examine the structure of this liquid metal at atomistic level. Time-resolved cluster analysis allows one to reveal that the short-range structural order in liquid gallium is determined by a range of the correlation lengths. This analysis performed over set of independent samples corre…
Dilute germanium carbides (Ge1-xCx) offer a direct bandgap for compact silicon photonics, but widely varying results have been reported. This work uses ab initio simulations with HSE06 hybrid functionals and spin-orbit coupling to study the Ge1-xCx band structure behavior in the absence of defects. Contrary to Vegard's law, the conduction band minimum at k=0 is consistently found to decrease with increasing C content, while L and X valleys change much more slowly. A vanishing bandgap was observed for all alloys with x>0.017. Conduction bands deviate from a constant-potential band anticrossing …
Lonsdaleite germanium has a direct band gap, but it is not an efficient light emitter due to the vanishing oscillator strength of electronic transitions at the fundamental gap. Transitions involving the second lowest conduction band are instead at least three orders of magnitude stronger. The inversion of the two lowest conduction bands would therefore make hexagonal germanium ideal for optoelectronic applications. In this work, we investigate the possibility to achieve this band inversion by applying strain. To this end we perform ab initio calculations of the electronic band structure and op…
Core-shell nanowires made of Si and Ge can be grown experimentally with excellent control for different sizes of both core and shell. We have studied the structural properties of Si/Ge and Ge/Si core-shell nanowires aligned along the $[110]$ direction, with diameters up to 10.2~nm and varying core to shell ratios, using linear scaling Density Functional Theory (DFT). We show that Vegard's law, which is often used to predict the axial lattice constant, can lead to an error of up to 1\%, underlining the need for a detailed \emph{ab initio} atomistic treatment of the nanowire structure. We analys…
In this work we report new silicon and germanium tubular nanostructures with no corresponding stable carbon analogues. The electronic and mechanical properties of these new tubes were investigated through ab initio methods. Our results show that the structures have lower energy than their corresponding nanoribbon structures and are stable up to high temperatures (500 and 1000 K, for silicon and germanium tubes, respectively). Both tubes are semiconducting with small indirect band gaps, which can be significantly altered by both compressive and tensile strains. Large bandgap variations of almos…
We report accurate, calculated electronic, transport, and bulk properties of zinc blende gallium arsenide (GaAs). Our ab-initio, non-relativistic, self-consistent calculations employed a local density approximation (LDA) potential and the linear combination of atomic orbital (LCAO) formalism. We strictly followed the Bagayoko, Zhao, and William (BZW) method as enhanced by Ekuma and Franklin (BZW-EF). Our calculated, direct band gap of 1.429 eV, at an experimental lattice constant of 5.65325 Å, is in excellent agreement with the experimental values. The calculated, total density of states data …
In this paper, we present new models of germanium selenide chalcogenide glasses heavily doped with silver. The models were readily obtained with ab initio molecular dynamics and their structure agrees closely with diffraction measurements. Thermal molecular dynamics simulation reveals the dynamics of Ag+ ions and the existence of trapping centers as conjectured in other theory work. We show that first principles simulation is a powerful tool to reveal the motion of ions in glass.
We present ab initio calculations of electronic and optical properties of perturbed hexagonal germanium and demonstrate that it is a superior material for active optoelectronic devices in the infrared spectral region. It is known that perfect lonsdaleite Ge is a pseudodirect semiconductor, i.e., with direct fundamental band gap but almost vanishing oscillator strength for the lowest-energy optical transitions. Perturbing the system by replacing a Ge atom in the unit cell with a Si atom boosts of the oscillator strength at the minimum direct gap by orders of magnitude, with a concurrent blue sh…
We present a first-principles study of bare and hydrogen passivated armchair nanoribbons of the puckered single layer honeycomb structures of silicon and germanium. Our study includes optimization of atomic structure, stability analysis based on the calculation of phonon dispersions, electronic structure and the variation of band gap with the width of the ribbon. The band gaps of silicon and germanium nanoribbons exhibit family behavior similar to those of graphene nanoribbons. The edges of bare nanoribbons are sharply reconstructed, which can be eliminated by the hydrogen termination of dangl…
We report results from an efficient, robust, ab-initio method for self-consistent calculations of electronic and structural properties of Ge. Our non-relativistic calculations employed a generalized gradient approximation (GGA) potential and the linear combination of atomic orbitals (LCAO) formalism. The distinctive feature of our computations stem from the use of Bagayoko-Zhao-Williams-Ekuma-Franklin (BZW-EF) method. Our results are in agreement with experimental ones where the latter are available. In particular, our theoretical, indirect band gap of 0.65 eV, at the experimental lattice cons…
Using ab-initio computational techniques on crystal determined clusters, we report on the similarities and differences of Al$_{50}$(C$_5$(CH$_3)_5)_{12}$, Ga$_{23}$(N(Si(CH$_3)_{3}$)$_{2}$)$_{11}$, and Au$_{102}$(SC$_7$O$_2$H$_5$)$_{44}$ ligand-protected clusters. Each of the ligand-protected clusters in this study show the similar stable character which can be described via a electronic shell model. We show here that the same type of analysis leads consistently to derive a superatomic electronic counting rule, independently of the metal and ligand compositions. One can define the cluster core…
We report on ab-initio calculations of the two-dimensional systems MoS2 and NbSe2, which recently were synthesized. We find that two-dimensional MoS$_2$ is a semiconductor with a gap which is rather close to that of the three dimensional analogue, and that NbSe$_2$ is a metal, which is similar to the three dimensional analogue of this compound. We further computed the electronic structure of the two-dimensional hexagonal (graphene like) lattices of Si and Ge, and compare them with the electronic structure of graphene. It is found that the properties related to the Dirac cone do not appear in t…
The response to compression of the clathrate type-II structure Ge(cF136) is investigated by means of \textit{ab initio} small-cell metadynamics at different temperatures and pressures. At lower pressure $p$=2.5 GPa the metastable metallic bct-5 phase competes against $β$-Sn Ge(tI4), which forms at higher pressures. On lowering temperature, the presence of amorphous intermediates obtained from Ge$_{136}$ is more pronounced and is instrumental to the formation of denser structural motifs, from which metallic bct-5 can form. Therein, anisotropic box fluctuations promote phase formation. The metad…
The coordination polyhedra around the cations are the building blocks of ionic solids. In context of amorphous InGaZn oxide (a-IGZO), even though the coordination polyhedra are irregularly arranged, it will be beneficial to identify them. In this work, we address the questions, (a) is it possible to classify all the polyhedra that occur in a-IGZO into only a few distinct groups? and (b) are these the same polyhedral motifs as those observed in the crystalline indium gallium zinc oxide (c-IGZO) or other related crystalline oxides of indium, gallium and zinc? Therefore, in this first principles …
Experimental advances in the fabrication and characterization of few-layer materials stacked at a relative twist of small angle have recently shown the emergence of flat energy bands. As a consequence electron interactions become relevant, providing inroads into the physics of strongly correlated two-dimensional systems. Here, we demonstrate by combining large scale ab initio simulations with numerically exact strong correlation approaches that an effective one-dimensional system emerges upon stacking two twisted sheets of GeSe, in marked contrast to all Moiré systems studied so far. This not …
The nanometer-scale size-dependent electronic transport properties of crystalline (c-) and amorphous (a-) germanium telluride (GeTe) ultrathin films sandwiched by titanium nitride (TiN) electrodes are investigated using ab initio molecular dynamics (AIMD), density functional theory (DFT), and Green's function calculations. We find that a-GeTe ultrathin films scaled down to about 38 Angstrom (12 atomic layers) still shows a band gap and the electrical conductance is mainly due to electron transport via intra-gap states. If the ultrathin films are further scaled, the a-GeTe band gap disappears d…
The phonon spectra of calcium, strontium, barium, radium, cadmium, zinc, magnesium, germanium, tin, and lead titanates with the perovskite structure are calculated from first principles within the density functional theory. By analyzing the unstable modes in the phonon spectra, the possible lattice distortions are determined and the energies of the corresponding phases are calculated. From analyzing the phonon spectra, force constants, and eigenvectors of TO phonons, a conclusion is drawn on the origin of the ferroelectricity in considered crystals. It is shown that the main factors determinin…
Complementary to the development of highly three-dimensional (3D) integrated circuits in the continuation of Moore's law, there has been a growing interest in new 3D deformation strategies to improve device performance. To continue this search for new 3D deformation techniques, it is essential to explore beforehand - using computational predictive methods - which strain tensor leads to the desired properties. In this work, we study germanium (Ge) under an isotropic 3D strain on the basis of first-principle methods. The transport and optical properties are studied by a fully ab initio Boltzmann…
High-quality defect-free lonsdaleite Si and Ge can now be grown on hexagonal nanowire substrates. These hexagonal phases of group-IV semiconductors have been predicted to exhibit improved electronic and optical properties for optoelectronic applications. While lonsdaleite Si is a well-characterized indirect semiconductor, experimental data and reliable calculations on lonsdaleite Ge are scarce and not consistent regarding the nature of its gap. Using ab initio density-functional theory, we calculate accurate structural, electronic, and optical properties for hexagonal Ge. Given the well-known …
Searches for low-energy tetrahedral polymorphs of carbon and silicon have been performed using density functional theory computations and the ab initio random structure searching (AIRSS) ap- proach. Several of the hypothetical phases obtained in our searches have enthalpies that are lower or comparable to those of other polymorphs of group 14 elements that have either been experimentally synthesized or recently proposed as the structure of unknown phases obtained in experiments, and should thus be considered as particularly interesting candidates. A structure of P bam symmetry with 24 atoms in…
The structural, electronic and dynamical properties of a group of 2D germanium-based compounds, including GeC, GeN, GeO, GeSi, GeS, GeSe, and germanene, are investigated by employing first-principles calculations. The most stable structure of each of these systems is identified after considering the most probable configurations and performing accurate phonon calculations. We introduce a new phase of germanene, which we name the tile germanene, which is significantly more stable than the known hexagonal germanene. We apply the modern modified Becke-Johnson (mBJ) and DFT1/2 schemes to obtain an …
Using {\it ab initio} total energy density-functional theory calculations, we investigate the electronic, structural and magnetic properties of Manganese doped Germanium nanowires. The nanowires have been constructed along the [110] direction and the dangling bonds on the surface have been saturated by hydrogen atoms. We observed that the Mn has lower formation energy at the center of the wire when compared to regions close to the surface. The Mn-Mn coupling has lower energy for a high-spin configuration except when they are first nearest neighbors. These results show that Ge:Mn nanowires are …
A new method for calculation of band structure has been proposed based on the Green's function theory and local sampling. Potential energy in the Hamiltonian of Schrodinger's equation is approximated with a series of sampled Dirac delta functions weighted by appropriate factors. These factors are found from multipole expansion of atomic potentials in the crystal lattice, with considering effects such as screening. Fourier transform was then applied to describe the wave function in reciprocal space. Sampling can be uniform or non-uniform throughout space; however rate and interval optimization …
Density-functional-theory (DFT) calculations have been performed on the Li-Si and Li-Ge systems. Lithiated Si and Ge, including their metastable phases, play an important technological rôle as Li-ion battery (LIB) anodes. The calculations comprise structural optimisations on crystal structures obtained by swapping atomic species to Li-Si and Li-Ge from the X-Y structures in the International Crystal Structure Database, where X={Li,Na,K,Rb,Cs} and Y={Si,Ge,Sn,Pb}. To complement this at various Li-Si and Li-Ge stoichiometries, ab initio random structure searching (AIRSS) was also performed. Betw…
Using combined experimental and computational approaches we show that at 43 GPa and 1300 K gallium phosphide adopts the super-Cmcm structure, here indicated with its Pearson notation oS24. First-principles enthalpy calculations demonstrate that this oS24 structure is more thermodynamically stable above about 20 GPa than other proposed polymorphs, such as cubic ZB and SC16 or the ubiquitous orthorhombic Cmcm phase (oS8). It is found that oS24-structured GaP exhibits short P-P bonds, according to our high-resolution structural analysis. Such phosphorous dimerization in GaP, observed for the firs…
Direct observation of strain and confinement shaping the hole subbands of Ge quantum wells
Eidgenossische Technische Hochschule Zürich（苏黎世联邦理工学院）；Paul Scherrer Institut（保罗谢尔研究所）；University of Basel（巴塞尔大学）；National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院新材料计算设计与发现国家中心（MARVEL））；University of Fribourg（弗里堡大学）
In recent years, there has been increasing interest in the specific heat $C$ of insulators and semiconductors because of the availability of samples with different isotopic masses and the possibility of performing \textit{ab initio} calculations of its temperature dependence $C(T)$ using as a starting point the electronic band structure. Most of the crystals investigated are elemental (e.g., germanium) or binary (e.g., gallium nitride) semiconductors. The initial electronic calculations were performed in the local density approximation and did not include spin-orbit interaction. Agreement betw…
We study the effect of semicore states on the self-energy corrections and electronic energy gaps of silicon, germanium and GaAs. Self-energy effects are computed within the GW approach, and electronic states are expanded in a plane-wave basis. For these materials, we generate {\it ab initio} pseudopotentials treating as valence states the outermost two shells of atomic orbitals, rather than only the outermost valence shell as in traditional pseudopotential calculations. The resulting direct and indirect energy gaps are compared with experimental measurements and with previous calculations base…
Raman and calorimetric studies on Ge_xSe_{1-x} glasses have provided evidence for the existence of the intermediate phase (IP) in chalcogenide and other glasses. Here, we present X-Ray Absorption Near Edge Structure (XANES) measurements on germanium selenide glasses in the IP composition range, and detect an electronic signature of the IP. Ab initio molecular dynamics (MD) based models of these glasses are discussed, and an atomistic picture of the IP, based upon the models and available experiments is presented. We show that these models reproduce detailed composition-dependent structure in t…
The power factor of pure p-type ZnSb has been calculated via ab initio simulations assuming that the carrier concentrations are due to the doping effect of intrinsic zinc vacancies. With a vacancy concentration close to the experimental solubility limit we were able to perfectly reproduce the Power Factor measured in polycrystalline ZnSb samples. The methodology has then been successfully extended for predicting the effect of extrinsic doping elements on the thermoelectric properties of ZnSb. Germanium and tin seem to be promising p-type doping elements. In addition, we give, for the first tim…
High Photovoltaic Efficiency in Bulk-Stacked One-Dimensional GeSe$_{2}$ van der Waals Crystal
Kyung Hee University（庆熙大学）；Korea Institute of Science and Technology Information (KISTI)（韩国科学技术信息研究院）；Korea Institute for Advanced Study (KIAS)（韩国高等科学研究院）；Kangwon National University（江原国立大学）；Hongik University（弘益大学）
We present exemplary results of extensive studies of mechanical, electronic and transport properties of covalent functionalization of graphene monolayers (GML) with -NH2. We report new results of ab initio studies of covalent functionalization of GML with -NH2 groups up to 12.5% concentration. Our studies are performed in the framework of the density functional theory (DFT) and non-equilibrium Green's function (NEGF). We discuss the stability (adsorption energy), elastic moduli, electronic structure, band gaps, and effective electron masses as a function of the density of the adsorbed molecule…
